Keywords

1 Introduction

Cold rolling is a form of cold working process performed below the recrystallization temperature. Undergoing multi-stage processing including pickling, cold rolling, heat treatment and coating, hot-rolled strip eventually transforms into cold-rolled products [1]. The majority of modern large-scale tandem cold mills characterized by large size, heavy load, continuous operation and automation, use oil film bearing as the heart of whole machine [2]. With the function to provide stable loading capacity for rolling process, oil film bearing has the feature of high working load, high operating speed, and harsh working environments [3]. If the running stability of the oil film bearing is compromised, their periodic errors would be beyond the compensation capability of various automatic control systems and directly impact the quality of the finished sheet. Furthermore, in case of an online burning incident in the oil film bearing, the entire mill would be forced to shut down, resulting in significant economic losses [4].

Consider a hybrid bearing with a design of double static pressure chambers for oil film bearing. The failure of one of the chambers will cause the clearance between sleeve and bush to tilt, accelerating the wear of Babbitt alloy [5], and indirectly reducing the service life of the bearing [6]. Therefore, ensuring the state of the static pressure chambers is particularly important. To ensure no leakage in the static pressure pipe system during each assembling process, a roller grinding workshop used to adopt a kind of conical tool recommended by Morgan Company to mutually support the upper and lower hydrostatic oil inlet, as a sealing measure. This method was effective when initially used, but after multiple uses, it caused certain damage to the inlet and resulted in the bump of nearby Babbitt alloy. The bump sealed off the inlet, causing severe negative impact. Morgan also recommends an online test method of the static pressure chamber using an online hydrostatic pump. However, this method occupies production time and is not accurate due to the mutual influence of the upper and lower rollers.

Besides, the clearance is a principal assembling parameter of the bearing. It plays a crucial role in load carrying, temperature rise and other factors during the operation of the bearing [7, 8]. So far, only the outer diameter of the sleeve and the inner diameter of the bush are measured in the workshop before assembling, while the actual assembling clearance after assembling is unable to measure. When the clearance is too small, the heat generated from the friction between the sleeve and bush accumulates continuously, causing sudden locking of the high-speed rotating roller immediately, thus causing burning accidents [9]. As the internal sleeves and bushes gradually age, most of the bushes in the workshop have undergone multiple repairs, leading to an increasing trend in the clearances. According to recent records for several years, the average number of sleeve damages per year is 19, and this number even skyrocketed to 28 in the last recorded year. What is particularly serious is that 8 of them were online damages, which bring out the shut-down of the machines to replace the support rollers. The total downtime reached 22 h during which the direct economic loss from sleeve repairs amounted to 2.05 million yuan. Therefore, it is necessary to propose a novel method for the static pressure pipe system test and the assembling clearance measuring, to avoid leakage in the system and master the corresponding relationship between actual assembling clearance and on-site use status.

2 Theory of Lubrication for Oil Film Bearing

Bearings are essential components in mechanical systems. Based on the hydrodynamic principles, once the shaft starts rotating, it continuously squeezes lubricating oil with a certain viscosity into the converging gap. As the shaft sucks the lubricating oil into the wedge-shaped gap, the compression of the oil generates distributed resistance, which is termed the hydrodynamic pressure [10]. When the sum of the hydrodynamic pressures in the load direction is able to balance the external load, a complete layer of pressure oil film is formed between the shaft and the bearing. The oil film causes the surfaces of the shaft and the bearing to separate from each other, therefore resulting in pure liquid friction. The whole process above is known as the hydrodynamic lubrication mechanism [11].

The fluid lubrication film that exists between Surface 1 and Surface 2, and the velocity of two surfaces are shown in Fig. 1. The Reynolds equation can be derived as follows from the velocity components U1, V1 and W1 on surface 1, and the velocity components U2, V2 and W2 on surface 2 [12]:

$$\frac{\partial }{\partial x}\left(\frac{{h}^{3}}{\eta }\frac{\partial p}{\partial x}\right)+\frac{\partial }{\partial y}\left(\frac{{h}^{3}}{\eta }\frac{\partial p}{\partial y}\right)=12\frac{\partial (\overline{U }h)}{\partial x}+12\frac{\partial h}{\partial t}$$
(1)

Here, \(\overline{U }=\frac{1}{2}({U}_{1}+{U}_{2})\), \(h={h}_{2}-{h}_{1}\), \(\eta\) represents the viscosity of the lubricating oil.

Fig. 1
A technical diagram depicting a 3-D element in a fluid flow field with differential forces and velocities. It includes pressure p and shear stress tau variables, along with their respective changes in the x and z directions.

The elemental body in the lubricating film experiences forces in the x-direction

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For oil film bearing, it is usually a fixed bearing and a rotating journal, implying that U1 = 0 and U2 = U. Considering the steady state situation, the Reynolds equation has the form which is commonly used in engineering:

$$\frac{\partial }{\partial x}\left(\frac{{h}^{3}}{\eta }\frac{\partial p}{\partial x}\right)+\frac{\partial }{\partial y}\left(\frac{{h}^{3}}{\eta }\frac{\partial p}{\partial y}\right)=6U\frac{\partial h}{\partial x}$$
(2)

Meanwhile, introduce the Reynolds boundary condition, assuming that the breakthrough of the oil film occurs at a divergent gap downstream from the minimum oil film thickness. At this point, the pressure and pressure gradient are both zero. So, the condition for complete termination boundary of the oil film is defined by:

$$p={p}_{a}, \;\; {\text{and}} \;\; \frac{\partial p}{\partial \alpha }=0$$
(3)

When adopting hybrid journal bearing as oil film bearing, the hybrid journal bearing is supplied with oil through hydrostatic system during the startup, braking or low-speed operation of the bearing. The hydrostatic oil film separates the Babbitt alloy layer on the surface of sleeve and bush, achieving the effect of hydrostatic levitation to improve performance of the bearing under low-speed operation [13]. As the rotational speed of the bearing gradually increases, the bearing reaches a hydrostatic-hydrodynamic hybrid lubrication state due to the oil film formation. During the operation of the bearing, static pressure is mainly utilized, while dynamic pressure act as a supplement to compensate for static pressure loss with hydrodynamic effect [14].

3 Test Method

The test method mainly consists of four parts, (1) static clearance test stand for oil film bearing, (2) electric-hydraulic control loading trolley, (3) loading trolley and (4) assembling clearance measuring module. Considering the complexity of the work environment in industrial sites, it is necessary to pre-layout the equipment involved in the testing method. In accordance with the dimensions obtained from surveying and mapping, a three-dimensional solid model of the work area is established as Fig. 2.

Fig. 2
A three-dimensional model of a setup has an assembly area with 3 cylindrical components components and a designated device placement area. Some smaller rectangular components are labeled 1, 2, and 3.

The three-dimensional tooling model for the test method

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Figure 3 shows the process of assembling clearance measuring. The oil film bearing is placed on a bracket after its complete assembly. Then, communicate the hydrostatic outlet of the electric-hydraulic control loading trolley with the hydrostatic inlet on the bearing seat through a hydraulic hose. The lubricating oil is injected by means of hydrostatic oil supply, to prevent the sleeve and bush from moving up and down, which would cause collisions and wear on roller. Simultaneously, push the loading trolley below the bearing seat, and output control commands through test stand to make the piston rod on the loading trolley move up and down, thereby driving the bearing seat to move similarly. When the roller is stationary, the displacement of the bearing seat from its natural resting position to the highest position shall be the target assembly clearance. The clearance value is calculated using a digital dial gauge installed on the bearing seat, which has remote transmission capability to measure the clearance.

Fig.3
An illustration of a setup has various rectangular, cylindrical, spherical, and trapezoidal machine parts, each with distinct textures indicating their material and type.

The schematic diagram for the assembling clearance measuring process

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3.1 Static Clearance Test Stand for Oil Film Bearing

As an operation terminal, the test stand is the primary human–machine interface device for performing test tasks and can collect test data in real-time. It is equipped with a computer analysis module inside for processing data, as well as a liquid crystal display with digital voltmeter display module on the front panel. The buttons on the control panel are responsible for process control throughout the entire test process. In addition, the test stand has a PLC control module and possesses data printing functionality.

3.2 Electric-Hydraulic Control Loading Trolley

The electric-hydraulic control loading trolley is a movable hydrostatic oil supply system that provides test pressure for various test conditions. According to the test requirements, the trolley needs to fulfill the following functions: be able to provide a pressure of 8 MPa for locking the oil film bearing; provide a pressure of 10 MPa for disassembling the bearing; and provide a pressure for static pressure test of the bearing, with a theoretically designed value of up to 80 MPa.

The principle diagram of the hydraulic system for the trolley is shown in Fig. 4. The maximum working pressure of the system reaches 80 MPa. The system uses a high-pressure ball valve to switch pressure between ultra-high and high, with the secondary pressure being controlled by a proportional relief valve to avoid the impact of primary pressure. The primary pressure is directly provided by a piston pump for the static pressure test. In terms of unloading, use the median function of electromagnetic directional valves for the process, with overflow valves serving as safety valves.

Fig. 4
A complex hydraulic circuit diagram featuring components like a double radial piston pump, electromagnetic directional valves, a high-pressure ball valve, a turbine flow sensor, and various pressure gauges, all interconnected to control flow and pressure.

The hydraulic principle diagram of the hydrostatic oil supply system

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The whole specific test process can be subdivided into 9 conditions with corresponding action sequence of each electromagnet under different states, as shown in Table 1. When pump 1–1 starts, electromagnet 7YA is energized and the system starts running in low pressure mode. The system remains in an unloading condition until any operation is performed. At this time, all electromagnets except for 7YA and 8YA are in a power-off state and all electromagnetic valves are in the median function state. Currently with the system being in condition 7, the system pressure can be adjusted by proportional relief valve 1–4. The states of all electromagnets in condition 2, 4 and 6 are same as those in condition 7.

Table 1 Sequence table for the actions of electromagnets
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When the system is loading for locking or disassembling, with three electromagnets adjusting the pressure, test oil passes through electromagnetic directional valves 1–2 and 1–5. Then, a power-on electromagnet 6YA would introduce the oil into the rodless chamber of locking cylinder 1–9, leading to condition 1; or a power-on electromagnet 5YA would introduce the oil into the rod side, leading to condition 3. In condition 5, three energized electromagnets adjust system pressure for static pressure test, ensuring that the test oil enters static pressure chamber 1–10. In condition 8, the system pressure is adjusted by a high-low pressure system consisting of overflow valves. The operations in condition 9 is similar to those in condition 5. When the oil pressure lifts the bearing seat, the head of the digital dial gauge moves accordingly, thus measuring the clearance.

3.3 Loading Trolley

If the loading pressure of the oil pressure control module is inadequate to lift the bearing seat, it is necessary to assist with the loading pressure output by the auxiliary oil pressure control module on the loading trolley. Owing to the load-bearing surface of the oil film bearing being on the underside, the force applied to the bearing seat by the loading trolley needs to be upward. The difference between the applied force and the self-weight of the bearing seat is balanced by the oil film pressure, which is supplied by hydrostatic system to avoid rigid contact between sleeve and bush.

4 Analysis of Test Result

This testing method has been conducted on-site at a cold rolling plant, as the photos in Fig. 5 show. Table 2 presents the relationship between the assembling clearance and burning accident. The following ten assembling clearance test values are listed, and the tracking records of whether there were burning accidents during the operation of the oil film bearing under these assembling clearances are provided.

Fig. 5
A large machine with cylindrical, spherical, and rectangular structure has labels for assembling clearance, loading trolley, and hydrostatic inlet. A rectangular device with a small screen has labels for electric-hydraulic control loading trolley and static clearance test stand.

The industrial site test photos

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Table 2 Table for the measurement results of the clearance between sleeve and bush
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For oil film bearings, the initial design value of assembling clearance is generally taken between 0.3 and 2.0‰ of the nominal diameter. The permissible range for the assembling clearance is between 0.2355 and 1.57 mm, calculated based on a 785 mm outer diameter of the sleeve. However, it needs to be noted that this range is too broad and vague so that it can only serve as a reference.

Figure 6 shows the actual data on assembling clearance collected using an offline test device for oil film bearing. There are a total of 33 assembling data points, with each point representing a clearance value. The triangles in Fig. 6 represent the clearance values where burning accidents occurred, while the dots represent the values without accidents. Taking 1.1 mm as the critical threshold, it is evident that all assembling clearance values resulting in burning accidents are below 1.1 mm. The 7 triangles in 21 data points indicate a staggering probability of 33.33% for burning accidents. In contrast, there have been no burning accident above 1.1 mm. Therefore, after analyzing with on-site engineers, it can be concluded that the danger zone for assembling clearance is below 1.1 mm, while the safe zone is above 1.1 mm. It is suggested to set the assembling clearance for oil film bearing starting from 1.1 mm, with an upper limit not exceeding the maximum value 1.4 mm in the diagram. If the safety factor is set to a larger value, it can be between 1.2 and 1.4 mm, but must not exceed 1.57 mm.

Fig. 6
A graph titled the actual condition of assembling clearance for oil film bearing plots clearance versus assembly times. As assembly times progress, data points shift from a safe zone to a danger zone, indicating increased risk of burning accidents.

The relationship between the assembling clearance and burning accident

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5 Conclusion

Here are a few suggestions for selecting assembling clearance between sleeve and bush:

  1. (1)

    Choose a smaller clearance of oil film bearing for low viscosity lubricating oil, a larger clearance for high viscosity lubricating oil. It is recommended to control the assembling clearance within 1.2–1.4 mm on the basis of practical test.

  2. (2)

    The flow rate of oil film bearing is directly proportional to the cube of the assembling clearance. A larger clearance means smaller fluid resistance, a larger flow rate and lower temperature rise inside the bearing, making it less prone to burn.

  3. (3)

    According to the dynamic pressure effect, the load capacity of oil film bearing is inversely proportional to the square of the assembling clearance, so the clearance should not be too large.

  4. (4)

    The \(pv\) value control of oil film bearing. With too little clearance, the deformation of the bearing itself cannot be fully accommodated by the bearing seat, resulting in the increase of \(pv\) value at the local contact point between the bearing and the roller, and an increased risk of burning.

In conclusion, it is a feasible solution to increase the minimum value of the assembling clearance from below 1.1 mm to above the safety threshold of 1.1 mm without exceeding the maximum clearance value, which can prevent the clearance from being in the danger zone. The clearance can be effectively controlled by the measuring device for the clearance between sleeve and bush.